Elemental concentration determination using neutron-induced activation gamma radiation

ABSTRACT

The present disclosure relates to borehole logging methods and apparatuses for estimating formation properties using nuclear radiation, particularly an apparatus and method for estimating amounts of silicon and/or oxygen in the formation. The method may include using nuclear radiation information from at least one nuclear radiation detector to estimate at least one parameter of interest. The method may include separating a gross nuclear radiation count into separate nuclear radiation components. The method may also include reducing an error in the estimated formation properties due to speed variations of a nuclear radiation source that activates the silicon and oxygen in the formation. The apparatus may include at least one nuclear radiation detector. The apparatuses may include an information processing device to perform the methods.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application claims priority from U.S. Provisional PatentApplication Ser. No. 61/379,711, filed on 2 Sep. 2010, incorporatedherein by reference in its entirety.

FIELD OF THE DISCLOSURE

In one aspect, this disclosure generally relates to borehole loggingmethods and apparatuses for estimating formation properties usingnuclear radiation based measurements. More particularly, this disclosurerelates to estimating one or more formation parameters of interest usinginformation obtained from a formation exposed to a neutron source.

BACKGROUND OF THE DISCLOSURE

Oil well logging has been known for many years and provides an oil andgas well driller with information about the particular earth formationbeing drilled. In conventional oil well logging, during well drillingand/or after a well has been drilled, a nuclear radiation source andassociated nuclear radiation detectors may be conveyed into the boreholeand used to determine one or more parameters of interest of theformation. A rigid or non-rigid carrier is often used to convey thenuclear radiation source, often as part of a tool or set of tools, andthe carrier may also provide communication channels for sendinginformation up to the surface.

SUMMARY OF THE DISCLOSURE

In aspects, the present disclosure is related to methods of estimatingat least one parameter of interest of a formation using induced gammaradiation detected from a subterranean formation.

One embodiment according to the present disclosure includes a method forestimating at least one parameter of interest of a formation,comprising: estimating the at least one parameter of interest byseparating nuclear radiation information into at least two nuclearradiation components.

Another embodiment according to the present disclosure includes anapparatus for estimating at least one parameter of interest of aformation, comprising: a carrier; at least one nuclear radiationdetector conveyed by the carrier and configured to generate informationrepresentative of nuclear radiation from an activated volume ofinterest; and an information processing device configured to estimatethe at least one parameter of interest by separating the generatednuclear radiation information into at least two nuclear radiationcomponents.

Another embodiment according to the present disclosure includes anon-transitory computer-readable medium product having stored thereoninstructions that, when executed by at least one processor, perform amethod the method comprising: estimating the at least one parameter ofinterest by separating information acquired from at least one nuclearradiation detector into at least two nuclear radiation components.

Examples of the more important features of the disclosure have beensummarized rather broadly in order that the detailed description thereofthat follows may be better understood and in order that thecontributions they represent to the art may be appreciated.

BRIEF DESCRIPTION OF THE DRAWINGS

For a detailed understanding of the present disclosure, reference shouldbe made to the following detailed description of the embodiments, takenin conjunction with the accompanying drawings, in which like elementshave been given like numerals, wherein:

FIG. 1 shows a schematic of a downhole tool deployed in a borehole alonga wireline according to one embodiment of the present disclosure;

FIG. 2 shows a flow chart of an estimation method for one embodimentaccording to the present disclosure;

FIG. 3 shows a graph of the (n,p) reaction cross section for oxygen-16;

FIG. 4 shows a graph of the (n,p) reaction cross section for silicon-28;

FIG. 5 shows a graphical illustration of the build-up of nitrogen-16 andaluminum-28 in a normalized sense when oxygen and silicon are exposed tothe at least one energy source;

FIG. 6 shows a graphical illustration of total radiation and individualradiation component decay using one embodiment according to the presentdisclosure;

FIG. 7 shows a flow chart of an estimation method for one embodimentaccording to the present disclosure;

FIG. 8 shows a graphical illustration of neutron flux on a volume ofinterest;

FIG. 9 shows a graphical illustration of tool speed variation from 15ft/min to 25 ft/min according to one embodiment of the presentdisclosure;

FIG. 10 shows a graphical illustration comparing normalized neutron fluxprofiles at a point of interest with a constant speed and increasingspeed energy source;

FIG. 11 shows a flow chart of an estimation method for one embodimentaccording to the present disclosure;

FIG. 12 shows a graphical illustration of estimated and predicted oxygencontents for a volume of interest according to one embodiment of thepresent disclosure; and

FIG. 13 shows a schematic of the apparatus for implementing oneembodiment of the method according to the present disclosure.

DETAILED DESCRIPTION

In aspects, this disclosure relates to estimating amounts of siliconand/or oxygen in a subterranean formation. The application of fastneutrons (over about 10 MeV for O-16) to the volume of interest of aformation may “activate” specific elements (such as silicon and oxygen).Herein, to “activate” an element means to bombard the element withneutrons so as to produce a radioactive isotope. For example, some ofthe oxygen-16, when struck by a neutron, may be transmuted intonitrogen-16 due to a neutron-proton reaction (where the atomic weightremains the same but the charge of the nucleus is reduced). In anotherexample, some of the silicon-28 may be changed to aluminum-28 through(n,p) reaction as well. Activation is not limited to neutron-protonreactions, as radiative capture (n,y) of thermal neutrons may also beused, such as for production of sodium-24 from sodium-23 and iodine-128from iodine-127. Activation may be initiated by an energy source, suchas a pulsed or constant neutron source, that may be conveyed in aborehole in proximity to the subterranean formation. The speed of anactive energy source while it is traveling in proximity to a volume ofinterest of the formation may determine the amount of activation thattakes place in the volume of interest. The response from the formationmay be in the form of prompt and/or delayed nuclear radiation, such asgamma rays from the radioactive decay of the isotopes, and the amount ofnuclear radiation may be a function of the amount of radioactiveisotopes present. Herein, nuclear radiation includes particle andnon-particle radiation emitted by atomic nuclei during nuclear processes(such as radioactive decay and/or nuclear bombardment), which mayinclude, but are not limited to, photons from neutron inelasticscattering and from neutron thermal capture reactions, neutrons,electrons, alpha particles, beta particles, and pair production photons.As such, the amount of specific elements present in the formation may beestimated using the amount of nuclear radiation detected from isotopesrelated to the specific elements, though the isotopes may not beisotopes of the specific elements. The amount of isotopes formed by theat least one energy source may vary with the amount of the specificelements present in the formation and the amount of exposure to the atleast one energy source.

For example, estimating the amount of silicon may use information from anuclear radiation detector that is indicative of gamma radiationresulting from the radioactive decay of aluminum-28. Herein,“information” may include raw data; processed data, analog signals, anddigital signals. The amount of aluminum-28 may, generally, be related tothe amount of silicon activated by the at least one energy source. Asthe at least one energy source moves through a borehole, exposure time,which may be independently measured or may be derived from speedinformation of the movement of the at least one energy source and/or theat least one nuclear radiation detector, may be recorded and used toestablish an exposure time for the volume of interest due to the atleast one energy source. Herein, “exposure times” may include (i) thetime period that the volume of interest is exposed to the active energysource, (ii) the time period that the at least one nuclear radiationdetector is exposed to nuclear radiation emitted by the volume ofinterest, and (iii) the intervening period between exposure of volume ofinterest and exposure of the at least one nuclear radiation detector bythe volume of interest. Exposure times may include the time period whenthe volume of interest or at least one nuclear detector are receivingnuclear radiation, regardless of whether the at least one energy sourceand/or the at least one nuclear detector are (i) stationary, (ii) movingat a constant speed, (iii) moving at a variable speed, or (iv) acombination thereof. Exposure times may be directly or indirectlyestimated. In some embodiments, one or more exposure times maybeestimated using one or more sensors located on the carrier, in theborehole, or at the surface. In some embodiments, exposure times foreach of the detectors may be estimated independently. In someembodiments, an exposure time may be estimated as a period of time wherethe at least one energy source or a detector is present in an exposurezone, where the exposure zone is a volume of space or a range (or band)along a path where the at least one energy source will irradiate thevolume of interest or the volume of interest will irradiate one or morenuclear radiation detectors. By relating the exposure time informationto the information acquired from at least one nuclear radiationdetector, the amount of silicon present in the formation may beestimated. A minimum rate or amount of radiation may be required toestablish when “exposure” is taking place. In some embodiments,“exposure” may be based on levels of naturally occurring radiationwithin the formation, such as when radiation from the source or volumeof interest is higher than background radiation levels, and/oroperational considerations. Using exposure time information to reduceerrors due to speed variations may be performed regardless of whetherthe average logging speed is high or low and whether the borehole ishorizontal, deviated, or vertical.

At low logging speeds, the amount of silicon may be estimated,generally, using nuclear radiation information acquired and, optionally,by compensating for variations in speed that alter exposure times of thevolume of interest. While, at higher logging speeds, speed variationsmay increase or decrease, these speed variations may still becompensated for by using exposure time information. However, higherlogging speeds may introduce additional nuclear radiation that may notbe present at low logging speeds. Basically, the nuclear radiationinformation acquired at higher logging speeds may be composed of morethan a single radiation component.

Faster logging may be desirable for efficiency at the wellsite, butresults in the detection of activation gamma rays from two or moreelements. The present disclosure provides methods for separation ofmultiple element signals at faster logging speeds. And determining bothsilicon and oxygen in a single pass may be more beneficial than justdetermining one or the other. Herein, the division between low and highlogging speeds is the point where the nuclear radiation detectors aremoving fast enough that, when the nuclear radiation detectors pass theactivated volume of interest, nuclear radiation contributions fromnitrogen-16 are significant to the overall nuclear radiation level.Determination of whether a nuclear radiation contribution is significantmay be based on, but not limited to, one or more of: (i) radiationcontribution by naturally occurring radioactivity in the formation, (ii)operational considerations, (iii) type or number of radiation detectorsused. In some embodiments, background radiation due to naturallyoccurring radioactive materials or activation of elements in the nuclearradiation detectors may be filtered out prior to separation of themultiple element signals. For example, a bismuth germinate (BGO)detector may generate its own gamma count due to activation of theoxygen in the BGO detector due to exposure to the at least one energysource.

As will be understood by those of skill in the art, nitrogen-16 has ahalf-life of about 7.13 seconds, while aluminum-28 has a half-life ofabout 134.5 seconds. The short half-life of nitrogen-16 leads to anitrogen-16 nuclear radiation component that will decrease much morequickly than the aluminium-28 nuclear radiation component. Hence, at lowlogging speeds, the nitrogen-16 nuclear radiation component may beinsignificant or too small to be effectively measured by the time the atleast one nuclear radiation detector in proximity to the volume ofinterest, thus only the aluminum-28 nuclear radiation component may beused. However, at high logging speeds, both nitrogen-16 and aluminum-28nuclear radiation components will be detectable. Thus, given thecharacteristics of the at least one energy source and the spacing of theone or more detectors, the threshold between low and high logging speedmay be the speed above which nuclear radiation from nitrogen-16 andaluminum-28 may be significant and below which only nuclear radiationfrom aluminum-28 may be significant. In the past, the overlappingnuclear radiation components may have interfered with the accuracy ofestimates of the amount of silicon in the formation. In general, if themeasurement is toward determining oxygen content, logging speed shouldbe high so that nitrogen-16 photons can be recorded before they decay toinsignificant levels. Since there will be photons from other activatedisotopes, nitrogen-16 counts can be determined only if they can beseparated from the total counts. If the measurement targets a slowerdecaying isotope, such as aluminum-28, the logging speed can be slowerto eliminate counts from nitrogen-16 decay but this may be go againstthe desire to finish the logging in a reasonable time frame.

An activated volume of interest may have several radioactive isotopes(radionuclides), which generate nuclear radiation that may be separatedusing methods and apparatuses disclosed in the present disclosure. Thus,the present disclosure provides methods and apparatuses for estimatingand separating nuclear radiation components of any one or more differentradionuclides (man-made or naturally occurring) at any logging speed.Some embodiments may include separating nuclear radiation componentsthat include, but are not limited to, two or more of: (i) nitrogen-16,(ii) neon-23, (iii) sodium-24, (iv) magnesium-27, (v) aluminum-28, (vi)manganese-56, (vii) cobalt-58, (viii) cobalt-60, and (ix) iodine-128. Insome embodiments, radiation information related to the two differentradionuclides may be separated using the different rates of radioactivedecay of each of the radionuclides. In other embodiments, the radiationinformation related to the two different radionuclides may be separatedusing energy spectrum information of the different radionuclides. Energyspectrum information may be separated using, but not limited to, one of:(i) deconvolution, (ii) stripping and (iii) a window technique or (iv) acombination of these techniques.

The present disclosure provides methods and apparatuses for performinglogging at high speeds by separating a gross nuclear radiation countinto separate components, thus each radioactive isotope may provide aradiation component. In the case of high logging speeds, the separatedcomponents may allow for the estimation of the amount of silicon and/oroxygen or others in the formation and in the tool body. The apparatusmay include at least one energy source and at least one nuclearradiation detector. In some embodiments, the at least one energy sourcemay be a nuclear radiation source, such as, but not limited to, one ormore of: (i) a pulsed neutron source and (ii) a constant neutron source.While nuclear radiation detectors may be used to detect nuclearradiation from the formation, the detectors are not limited to detectingnuclear radiation of the same type as emitted by the at least one energysource. The at least one detector may have shielding to prevent thecounting of nuclear radiation from unintended sources. Logging mayinclude, but is not limited to, acquiring information for estimating oneor more of: (i) a silicon content, (ii) an oxygen content, (iii) asodium content, (iv) an iodine content, and (v) an iron content, (vi) analuminum content, and (vii) a magnesium content.

The present disclosure also provides methods and apparatuses forestimating at least one parameter of interest in a formation usingoxygen content information and at least a formation lithology. Lithologymay include mineralogy, combinations of mineralogies, rockcharacteristics, rock structure, and rock composition. For the purposesof this disclosure, lithology does not include porosity. For example, inone embodiment, water saturation may be estimated using oxygen contentinformation along with the formation lithology. Content information mayinclude, but is not limited to, one or more of: (i) absoluteconcentration, (ii) relative concentration, (iii) ratio by volume, (iv)ratio by mass, and (v) mass. Oxygen content may be estimated usingprompt and/or delayed gamma rays from neutron inelastic scatteringand/or gamma rays from oxygen activation based on either time spectrumand/or energy spectrum of gamma rays from those reactions and othertechniques known to those of skill in the art. As different minerals andmineral combinations have different amounts of oxygen, the formationlithology may be used to establish a model that may be used to estimatethe water saturation using the oxygen content. The model may include atleast one predicted value for comparison with an estimated oxygencontent. In some embodiments, the estimation of water saturation mayinclude using porosity information in addition to estimated oxygencontent and formation lithology.

In one embodiment, the model may include a predicted maximum value and apredicted minimum value for the oxygen content for a formationlithology. The estimated oxygen content may be compared with thepredicted maximum value for oxygen and the predicted minimum value foroxygen, and this comparison may be used to estimate a value for watersaturation in the formation. In some embodiments, water saturation maybe estimated using a model that comprises a linear or non-linearrelationship (depending on the formation lithology) between thepredicted maximum value for oxygen and the predicted minimum value foroxygen, where the position of the oxygen content along the curve mayprovide the estimated water saturation. The curve may be linear ornon-linear. In some embodiments where the model is linear, the value ofwater saturation may be estimated by the formula:

${S_{w} = {\frac{\left( {O_{measured} - O_{oil}} \right)}{\left( {O_{water} - O_{oil}} \right)} = \frac{O_{measured} - O_{oil}}{\Delta\; O}}},$where S_(w) is the value of water saturation, O_(measured) is the valueof estimated oxygen content, O_(oil) is the predicted minimum value foroxygen content, O_(water) is the predicted maximum value for oxygencontent, and ΔO is the size of the range between the predicted maximumand predicted minimum values for oxygen.

The water saturation may be estimated based on the relative position ofthe estimated oxygen content within a range of possible oxygen levels.This estimate may be clarified based on variations in formationcharacteristics (e.g., lithology). FIG. 1 schematically illustrates adrilling system 10 having a downhole tool 100 configured to acquireinformation for estimating at least one parameter of interest of aformation 180. In one illustrative embodiment, the tool 100 may containan energy source 140 and associated detectors 120, 130. Some embodimentsmay include multiple energy sources spaced along the longitudinal axisof the borehole 150. The use of two detectors is exemplary andillustrative only, as some embodiments may use a single detector. Thesystem 10 may include a conventional derrick 160 erected on a derrickfloor 170. A carrier 110, which may be rigid or non-rigid, may beconfigured to convey the downhole tool 100 into borehole 150 inproximity to formation 180. The carrier 110 may be a drill string,coiled tubing, a slickline, an e-line, a wireline, etc. Downhole tool100 may be coupled or combined with additional tools (e.g., some or allthe information processing system of FIG. 11). Thus, depending on theconfiguration, the tool 100 may be used during drilling and/or after theborehole 150 has been formed. The nuclear radiation source 140 emitsnuclear radiation into the volume of interest 185 of the formation 180to be surveyed. This nuclear radiation interacts with the nuclei of theatoms of the material of the formation to produce new isotopes as aresult of various nuclear reactions and causing the release of at leastone of: (i) inelastic gamma rays and (ii) capture gamma rays. Inelastic,capture gamma rays and gamma rays from the decay of activation productswill, in turn, undergo Compton scattering and pair production reactionsand will generate a secondary gamma ray source. In one embodiment, thedownhole tool 100 may use a pulsed neutron generator emitting 14.2 MeVfast neutrons as its energy source 140. The use of 14.2 MeV neutronsfrom a pulsed neutron source is illustrative and exemplary only, asdifferent energy levels of neutrons may be used; energy source 140 maybe continuous for some embodiments. In some embodiments, the at leastone energy source 140 may be controllable in that the nuclear radiationsource may be turned “on” and “off” while in the borehole, as opposed toa nuclear radiation source that is “on” continuously. Due to theintermittent nature of the nuclear radiation source, the inelastic andcapture photons created will reach the detectors 120, 130 duringdifferent time periods. Inelastic photons are generated predominantlyduring the pulse, while capture photons are generated during and afterthe pulse. Although gamma rays from decay of the activation products canbe recorded all along, they will be separated from inelastic and capturegamma rays in time periods where enough time elapsed for all thermalneutron capture reactions to die away.

The detectors 120, 130 provide signals that may be used to estimate thenuclear radiation count returning from the formation. Generally,detectors 120, 130 are spaced in a substantially linear fashion relativeto the nuclear radiation source along the longitudinal axis of theborehole. If two detectors are used, there may be a short spaced (SS)detector and a long spaced (LS) detector, wherein the detectors havedifferent distances from the nuclear radiation source. For instance, inone embodiment, detector 130 may be a short spaced detector, anddetector 120 may be a long spaced detector. The SS and LS detectors arenot limited to being placed on the same side of the nuclear radiationsource and their spacing from the nuclear radiation source may be thesame or different. In some embodiments, at least one detector 120, 130may be co-located with the at least one energy source 140. Additionaldetectors may be used to provide additional nuclear radiationinformation. At least one of the detectors may be a gamma ray detector.Nuclear radiation shielding (not shown) may be located between energysource 140 and the detectors 120, 130. Nuclear radiation shielding mayinclude, but is not limited to, gamma-ray shielding and neutronshielding. Drilling fluid 190 may be present between the formation 180and the downhole tool 100, such that emissions from energy source 140may pass through drilling fluid 190 to reach formation 180 and nuclearradiation induced in the formation 180 may pass through drilling fluid190 to reach the detectors 120, 130. In some embodiments, electronics(not shown) associated with the detectors may be capable of recordingcounts from axially spaced detectors 120, 130.

FIG. 2 shows, in flow chart form, an exemplary method 200 according tothe present disclosure for estimating at least one parameter of interestof the formation 180 (FIG. 1) using a model based on informationacquired from the two nuclear radiation detectors 120, 130 (FIG. 1).Referring now to FIGS. 1 and 2, method 200 may include step 210, wherethe at least one energy source 140 emits a nuclear radiation pulse (suchas a neutron pulse) in proximity to a volume of interest 185 of theformation 180. In step 220, the resulting interactions between the pulseand the material of the formation result in nuclear radiation that maybe detected by the nuclear radiation detectors 130, 120 as the detectors120, 130 move past, or in proximity to, the volume of interest 185. Thedetectors 120, 130 may produce a signal with the nuclear radiationinformation acquired from the volume of interest 185. Herein, theneutron interactions may include, but are not limited to, elastic andinelastic scattering, thermal neutron capture, neutron-proton (n,p)reactions and gamma ray interactions include pair production, Comptonscattering, Raleigh scattering, and the photoelectric effect. In step230, the information may be separated into separate nuclear radiationcomponents, which may represent gamma rays from nitrogen-16 andaluminum-28. In step 240, the separate nuclear radiation components maybe used to estimate the amounts of silicon and/or oxygen present in thevolume of interest 185. In some embodiments, where the logging speed isslow enough that nitrogen-16 nuclear radiation component hassignificantly decreased before the detectors reach the volume ofinterest 185, step 230 may not be performed and step 240 may onlyinvolve estimating the amount of silicon using a single nuclearradiation component.

Turning to method 200 in more detail, the at least one energy source 140may be activated in step 210 at t=t₀ to build-up radioactive isotopes inthe volume of interest 185. This build-up may last from t₀ to t₁ whereelements may be activated based on the energy flux used to activate theelements. For example, FIG. 3 shows the reaction cross section of oxygenwhere curve 310 indicates the activation of oxygen based on energylevel, and FIG. 4 shows the reaction cross section for silicon wherecurve 410 indicates the activation of silicon based on energy level. Ascan be seen in FIGS. 3 & 4, the energy flux used may need to be aboveapproximately 10.5 MeV in order for both oxygen and silicon to beactivated. Curves 310 and 410 show that silicon activation begins atlower energy levels than oxygen activation.

During the build-up period, the isotopes may be activated at differentrates, as shown in FIG. 5. Curve 510 indicates the build-up nitrogen-16due to oxygen activation; and curve 520 indicates the build-up ofaluminum-28 due to silicon activation. At t=t₁, the at least one energysource 140 may be deactivated, which effectively pauses the applicationof neutrons to generate more radioactive isotopes. The radioactiveisotopes production term due to exposure to the at least one energysource 140 may be estimated by multiplying the energy flux (such asneutron flux) and the reaction cross section of the volume of interestin the formation such that:Q(t)=∫_(E) _(min) ^(∝)∫_(V)ϕ(t,r,E)Σ( r,E)dEdr   (1)

Therefore, in the case of nitrogen-16 build-up from oxygen,

$\begin{matrix}{Q_{N - 16} =_{7}^{16}{N{\mspace{11mu}\;}\text{production~~rate}}} \\{{= {\int_{E}{\int_{V}{{\Sigma_{p}\left( {\overset{\_}{r},E} \right)}{\phi\left( {t,\overset{\_}{r},E} \right)}d\overset{\_}{r}{dE}}}}},{\mspace{275mu}\;}(2)} \\{{= {\int{\int{{\sigma_{p,{0 - 16}}(E)}{N_{O - 16}\left( \overset{\_}{r} \right)}{\phi\left( {t,\overset{\_}{r},E} \right)}d\overset{\_}{r}{dE}}}}},\mspace{169mu}(3)}\end{matrix}$

and for constant N-16 production rates, N-16 nuclear density at t=t₁ is

$\begin{matrix}{{{N_{N - 16}(t)} = {\frac{Q_{N - 16}}{\lambda_{N - 16}}\left\lbrack {1 - e^{\lambda_{N - 16}{({t_{1}\mspace{14mu} t_{0}})}}} \right\rbrack}},} & (4)\end{matrix}$where,

N_(N-16)=₇ ¹⁶N nuclear density,

λ_(N-16)=₇ ¹⁶N decay constant, and

σ_(p,O-16)=O-16 microscopic (n,p)cross section

In the case of aluminum-28 build-up from silicon-28,

$\begin{matrix}{{Q_{{Al} - 28} = {{{\,_{13}^{28}{Al}}\mspace{14mu}{production}\mspace{14mu}{rate}}\mspace{70mu} = {\int_{E}{\int_{V}{\sum_{p}{\left( {\overset{\_}{r},E} \right){\phi\left( {t,\overset{\_}{r},E} \right)}d\overset{\_}{r}{dE}}}}}}},} & (5) \\{\mspace{70mu}{{= {\int_{E}{\int_{V}{{\sigma_{,{{Si} - 28}}(E)}{N_{{Si} - 28}\left( \overset{\_}{r} \right)}{\phi\left( {t,\overset{\_}{r},E} \right)}d\overset{\_}{r}{dE}}}}},{and}}} & (6) \\{{N_{{Al} - 28}\left( t_{1} \right)} = {\frac{Q_{{Ai} - 28}}{\lambda_{{Al} - 28}}\left\lbrack {1 - e^{\lambda_{{Al} - 28}{({t_{1} - t_{0}})}}} \right\rbrack}} & (7)\end{matrix}$where,

N_(Al-28)=₁₃ ²⁸Al nuclear density,

λ_(Al-28)=₁₃ ²⁸Al decay constant,and

σ_(p,Si-28)=Si-28 microscopic (n,p) reaction cross section

After build-up ends when t=t₁, the radioactive component due to simpledecay at t=t₂ may be expressed as:N_(N-16)(t ₂)=N_(N-16)(t ₁)e ^(−λ) ^(N-16) ^((t) ² ^(-t) ¹ ⁾  (8)N_(Al-28)(t ₁)=N_(Al-28)(t ₁)e ^(−λ) ^(Al-28) ^((t) ² ^(-t) ¹ ⁾  (9)

As the near (first) detector 130 take a reading at t=t₂ and the far(second) detector 120 takes a reading at t=t₃, the relative distributionof gamma photons coming from nitrogen-16 and aluminum-28 will bedifferent. As shown in FIG. 6, the count 610 of nitrogen-16 gammaphotons and the count 620 of aluminum-28 photons may be combined to forma gross nuclear radiation count 630, which is detected by the nuclearradiation detectors. The nitrogen-16 and aluminum-28 nuclear radiationcomponents 610, 620 may be separated in step 230.

Where

A₁=data from 1st detector

A₂=data from 2nd detector

λ_(x)=₇ ¹⁶N decay constant

λ_(y)=₁₃ ²⁸Al decay constant

A_(1x)=Counts from ₇ ¹⁶N at t=t₂,

A_(2x)=Counts from ₇ ¹⁶N at t=t₃,

A_(1y)=Counts from ₁₃ ²⁸Al at t=t₂,

A_(2y)=Counts from ₁₃ ²⁸Al at t=t₃, and

Δt=t₃−t₂;

then the nuclear radiation counts may be expressed as:A ₁ =A _(1x) +A _(1y)  (10)andA ₂ =A _(2x) +A _(2y)  (11).The counts from the detectors at t=t₃ may be expressed as function ofcounts at t=t₂ such thatA _(2x) =A _(1x) e ^(−λ) ^(x) ^(Δt)  (12)andA _(2y) =A _(1y) e ^(λ) ^(y) ^(Δt)  (13).

Eqns. (12) and (13) may be substituted into Eqns. (10) and (11) asfollows:A ₁ =A _(1x) +A _(1y)  (14)A ₂ =A _(1x) e ^(−λ) ^(x) ^(Δt) +A _(1y) e ^(−λ) ^(y) ^(Δt)  (15).Then Eqn. (13) may be used to provide A_(1x) to Eqn. (14) to produceA ₂=(A ₁ −A _(1y))e ^(−λ) ^(x) ^(Δt) +A _(1y) e ^(−λ) ^(y) ^(Δt)  (16).Solving for A_(1y),

$\begin{matrix}{{A_{1y}\left\lbrack {e^{{- \lambda_{y}}\Delta\; t} - e^{{- \lambda_{x}}\Delta\; t}} \right\rbrack} = {A_{2} - {A_{1}e^{{- \lambda_{x}}\Delta\; t}}}} & (17) \\{A_{1y} = {\frac{A_{2} - {A_{1}e^{{- \lambda_{x}}\Delta\; t}}}{e^{{- \lambda_{y}}\Delta\; t} - e^{{- \lambda_{x}}\Delta\; t}}.}} & (18)\end{matrix}$Thus A_(1x) may also be obtained as:A _(1x) =A ₁ −A _(1y)  (19)

In step 240, the nuclear radiation counts due to the decay ofnitrogen-16 and/or aluminum-28 may be used to estimate the amounts ofoxygen and silicon. Generally, if number of decays can be correlated tothe nuclear density for a specific nuclide by dividing the decay rate bythe decay constant. In that regard, The nuclear density of nitrogen-16at t=t₂N_(N-16)(t ₂)=N_(N-16)(t ₁)e ^(−λ) ^(N-16) ^((t) ² ^(-t) ¹ ⁾  (20)

may be expressed in terms of t=t₁,N_(N-16)(t ₂)=N_(N-16)(t ₂)e ^(λ) ^(N-16) ^((t) ² ^(-t) ¹ ⁾  (21),

and the nuclear density of aluminum-28 at t=t₂N_(Al-28)(t ₂)=N_(Al-28)(t ₁)e ^(−λ) ^(Al-28) ^((t) ² ^(-t) ¹ ⁾  (22),

may be expressed in terms of t=t₁,N_(Al-28)(t ₂)=N_(Al-28)(t ₁)e ^(λ) ^(Al-28) ^((t) ² ^(-t) ¹ ⁾  (23).Using the build-up equation

$\begin{matrix}{\mspace{20mu}{{{\left. {N_{N - 16}\left( t_{1} \right)} \right.\sim\;\frac{q_{N - 16}}{\lambda_{N - 16}}}\left\lfloor {1 - e^{- {\lambda_{N - 16}{({t_{1} - t_{0}})}}}} \right\rfloor},\mspace{20mu}{and}}} & (24) \\{{\left. {N_{N - 16}\left( t_{1} \right)} \right.\sim\;{\frac{\int{\int{{r_{p,o}(E)}{N_{O - 16}\left( \overset{\_}{r} \right)}{\phi\left( {t,\overset{\_}{r},E} \right)}d\overset{\_}{r}{dE}}}}{\lambda_{N - 16}}\left\lbrack {1 - e^{- {\lambda_{N - 16}{({t_{2} - t_{0}})}}}} \right\rbrack}}.} & (25)\end{matrix}$A time independent constant shape for ϕ(r,E) and a homogeneous formationmay yield

$\begin{matrix}{{N_{N - 16}\left( t_{1} \right)} = {{\frac{{VN}_{O - 16}{\int{{r_{p}(E)}{\phi(E)}{dE}}}}{\lambda_{N - 16}}\left\lbrack {1 - e^{- {\lambda_{N - 16}{({t_{1} - t_{0}})}}}} \right\rbrack}.}} & (26)\end{matrix}$By defining a constant, C_(O-16),C_(O-16) −VN _(O-16) ∫r _(p)(E)ϕ(E)dE  (27),then the oxygen and silicon concentrations in the formation can beestimated by using the expressions given by equations (28) and (29).

$\begin{matrix}{{{\left. N_{O - 16} \right.\sim C_{O - 16}}\;\frac{\;{\lambda_{N - 16}{N_{N - 16}\left( t_{1} \right)}}}{\left\lbrack {1 - e^{- {\lambda_{N - 16}{({t_{1} - t_{0}})}}}} \right\rbrack}}{and}} & (28) \\{{\left. N_{{Si} - 28} \right.\sim C_{{Si} - 28}}\;{\frac{\lambda_{{Al} - 28}{N_{{Al} - 28}\left( t_{1} \right)}}{\left\lbrack {1 - e^{- {\lambda_{{Al} - 28}{({t_{1} - t_{0}})}}}} \right\rbrack}.}} & (29)\end{matrix}$

FIG. 7 shows, in flow chart form, an exemplary method 700 according tothe present disclosure for estimating at least one parameter of interestof the formation 180 (FIG. 1) using a model based on informationacquired from at the two gamma ray detectors 120, 130 (FIG. 1).Referring now to FIGS. 1 and 7, method 700 may include step 710, wherethe at least one energy source 140 emits a nuclear radiation pulse inproximity to a volume of interest 185 of the formation 180. In step 720,the resulting interactions between the pulse and the material of theformation result in nuclear radiation that may be detected by thenuclear radiation detectors 130, 120 as the nuclear radiation detectors120, 130 move past, or in proximity to, the volume of interest 185. Thedetectors 120, 130 may produce a signal with the prompt and/or delayednuclear radiation information acquired from the volume of interest 185.In step 730, the information may be modified using exposure timeinformation for the at least one energy source 140 and/or the detectors120, 130 to compensate for uneven activation of silicon and oxygen inthe volume of interest 185 of the formation. In step 740, the at leastone parameter of interest may be estimated using the modifiedinformation.

Throughout the build-up, the at least one energy source 140 may bemoving along the borehole 150. The build-up in portions of the volume ofinterest 185 may be affected by variations in the energy flux, such asdue to changes in the speed and to changes in the distance between thevolume of interest 185 and the at least one energy source 140. In someembodiments, the time dependent neutron flux profile may be approximatedby assuming flux distribution in a Gaussian shape, though fluxdistributions may occur in other shapes, as a function of distancebetween the volume of interest 185 and the at least one energy source140 as shown in curve 810 of FIG. 8. However, the shape of the flux maybe affected by variations in speed of the at least one energy source 140and/or the nuclear radiation detectors 120, 130 as approximated usingthe formulas:

$\begin{matrix}{{\frac{dN}{dt} = {{{- \lambda}\;{N(t)}} + {Q(t)}}},{and}} & (30) \\{{N(t)} = {{{N\left( t_{0} \right)}e^{{- \lambda}\; t}} + {e^{{- \lambda}\; t}{\int_{t_{v}}^{t}{{Q\left( t^{\prime} \right)}e^{\lambda\; t^{\prime}}{dt}^{\prime}}}}}} & (31)\end{matrix}$where nuclear reaction rate profile, Q(t), has a Gaussian shape in timedue to the flux profile. Since most of the nuclides used in formationevaluation decay quite rapidly, we may safely assume that there were notany of those present in the formation to begin with. In that case, weassume the terms N(t)=0 at t=t₀.

In step 730, the effects of variations of speed of the at least oneenergy source and/or at least one nuclear radiation detector may bereduced. In one embodiment, the speed of the at least one energy sourcemay be modeled mathematically. The use of mathematical model isillustrative and exemplary only, as other models may be used as known bythose of skill in the art. FIG. 9 shows a mathematical model of thespeed of the at least one energy source 140 using a second orderpolynomial,v(t)=at ² +bt+c  (32),

so that the speed variations may be seen in curve 910.

Thus, the distance traveled by the at least one energy source 140 for agiven time frame is

$\begin{matrix}{{Z = {{\int_{t_{0}}^{t}{\left\lbrack {{at}^{2} + {bt} + c} \right\rbrack{dt}}} = {{\frac{{at}^{3}}{3} + \frac{{bt}^{2}}{2} + {ct} + d}❘_{t_{0}}^{t}{.{Thus}}}}},} & (33) \\{{Z = {\frac{{at}^{3}}{3} + \frac{{bt}^{2}}{2} + {ct} + Z_{m\; i\; n}}}{{{when}\mspace{14mu} t_{0}} = 0.}} & (34)\end{matrix}$Substituting Z for t in Q(t) yields

$\begin{matrix}{{Q(Z)} = {e^{{eZ}^{2}} = {e^{{e\lbrack{\frac{{at}^{3}}{3} + \frac{{bt}^{2}}{2} + {ct} + Z_{m\; i\; n}}\rbrack}^{2}}.}}} & (35)\end{matrix}$Then N(t) may be determined,

$\begin{matrix}\begin{matrix}{{N(t)} = {e^{{- \lambda}\; t}{\int_{t_{0}}^{\tau}{{Q\left( t^{\prime} \right)}e^{\lambda\; t^{\prime}}{dt}^{\prime}}}}} \\{= {e^{{- \lambda}\; t}{\int{e^{{e{\lbrack{\begin{matrix}{at}^{3} \\3\end{matrix} + \begin{matrix}{bt}^{2} \\2\end{matrix} + {ct} + Z_{m\; i\; n}}\rbrack}}^{2}}e^{\lambda\; t}{{dt}.}}}}}\end{matrix} & (36)\end{matrix}$

The speed of the at least one energy source 140, which may be determinedfrom the speed of the tool on which the at least one energy source isoperably connected, may be used to estimate the values of coefficientsa, b, c, and e. In some embodiments, the values of coefficients a, b, cand e may be estimated using the speed of the at least one nuclearradiation detector. In another embodiment, the coefficients may beestimated using the speed of the at least one energy source and of atleast one nuclear radiation detector. In yet another embodiment, thecoefficients may be determined using exposure time information, whichmay be derived from speed information or obtained independently. FIG. 10shows the variations in energy flux at the volume of interest 185 basedan assumed constant speed 1010 and with correction for speed variation1020.

Since there may not be further build-up beyond t₁, the nuclear densitiesof nitrogen-16 and aluminum-28 may be set as follows:

$\begin{matrix}{{N_{N - 16}\left( t_{1} \right)} = {e^{{- \lambda_{N - 16}}t_{1}}{\int_{t_{0}}^{t_{1}}{e^{{e_{N - 16}\lbrack{\frac{a_{N - 16}t^{3}}{3} + \frac{b_{N - 16}t^{2}}{2} + {c_{N - 16}t} + Z_{m\; i\; n}}\rbrack}^{2}}e^{\lambda_{N - 16}t}{dt}}}}} & (36) \\{{N_{{Al} - 28}\left( t_{1} \right)} = {e^{{- \lambda_{{Al} - 28}}t_{1}}{\int_{t_{0}}^{t_{1}}{e^{{e_{{Al} - 28}\lbrack{\frac{a_{{Al} - 28}t^{3}}{3} + \frac{b_{{Al} - 28}t^{2}}{2} + {c_{{Al} - 28}t} + Z_{m\; i\; n}}\rbrack}^{2}}e^{\lambda_{{Al} - 28}t}{dt}}}}} & (37)\end{matrix}$

In some embodiments, elements of method 200 and elements of method 700may be combined such that the at least one parameter of interest may beestimated using nuclear radiation information that has been modified tocompensate for speed variations and separated into at least tworadiation components.

FIG. 11 shows, in flow chart form, an exemplary method 1100 according tothe present disclosure for estimate at least one parameter of interestof the formation 180 (FIG. 1) using an oxygen content value. In, step1110, a value for oxygen content may be estimated for a volume ofinterest of a formation. In step 1120, at least one predicted value foroxygen content of the volume of interest based on the formationlithology may be obtained. In some embodiments, the at least one valuefor oxygen content of the volume of interest may be a predicted minimumvalue for oxygen and a predicted maximum value for oxygen in the volumeof interest based on formation lithology. In some embodiments, thepredicted maximum value for oxygen may correspond to a water-filledporosity for the volume of interest, and the predicted minimum value foroxygen may correspond to an oil-filled porosity for the volume ofinterest. The at least one predicted value may be obtained throughdirect measurement, indirect measurement, historical analysis,interpolation, professional expertise, modeling, or combinationsthereof. In some embodiments, the at least one predicted value may bemodified using information regarding one or more of: (i) changes inborehole size, (ii) completion hardware, (iii) clay type, and (iv)lithology, (v) source speed, (vi) source intensity. In step 1130, avalue for water saturation may be estimated using a comparison of theestimated value for oxygen content and the at least one predicted valuefor oxygen content.

FIG. 12 shows a graphical representation of a predicted minimum valuefor oxygen content and a predicted maximum value for oxygen content fora formation with a certain lithology. Shown are gamma counts associatedwith sandstone (SS) limestone (LS) where the volume of interest 185 isactivated. Curve 1210, (100% W SS), illustrates the nuclear radiationcount for sandstone when 100 percent water is present in the pores ofthe formation. Curve 1220, (100% O SS), illustrates the nuclearradiation count for sandstone when 100 percent oil is present in thepores of the formation. Curve 1230, (100% W LS), illustrates the nuclearradiation count for limestone when 100 percent water is present in thepores of the formation. Curve 1240, (100% O LS), illustrates the nuclearradiation count for limestone when 100 percent oil is present in thepores of the formation. Point 1250 represents the estimated oxygencontent. Range 1260 is the band between 100 percent water curve 1220 and100 percent oil curve 1240 (ΔO) limestone. Finally, range 1270 is thedifference between the estimated oxygen content and the 100 percent oilcurve 1240. In one embodiment, a value for water saturation may beestimated using the size of range 1270 and the size of range 1260. WhileFIG. 12 describes an embodiment of the present disclosure in terms oflimestone and sandstone, this is exemplary and illustrative only, asembodiments will also work with dolomite, other mineralogies, andcombinations of mineralogies.

As shown in FIG. 13, certain embodiments of the present disclosure maybe implemented with a hardware environment that includes an informationprocessor 1300, a information storage medium 1310, an input device 1320,processor memory 1330, and may include peripheral information storagemedium 1340. The hardware environment may be in the well, at the rig, orat a remote location. Moreover, the several components of the hardwareenvironment may be distributed among those locations. The input device1320 may be any information reader or user input device, such as datacard reader, keyboard, USB port, etc. The information storage medium1310 stores information provided by the detectors. Information storagemedium 1310 may be any standard non-transitory computer informationstorage device, such as a ROM, USB drive, memory stick, hard disk,removable RAM, EPROMs, EAROMs, EEPROM, flash memories, and optical disksor other commonly used memory storage system known to one of ordinaryskill in the art including Internet based storage. Information storagemedium 1310 stores a program that when executed causes informationprocessor 1300 to execute the disclosed method. Information storagemedium 1310 may also store the formation information provided by theuser, or the formation information may be stored in a peripheralinformation storage medium 1340, which may be any standard computerinformation storage device, such as a USB drive, memory stick, harddisk, removable RAM, or other commonly used memory storage system knownto one of ordinary skill in the art including Internet based storage.Information processor 1300 may be any form of computer or mathematicalprocessing hardware, including Internet based hardware. When the programis loaded from information storage medium 1310 into processor memory1330 (e.g. computer RAM), the program, when executed, causes informationprocessor 1300 to retrieve detector information from either informationstorage medium 1310 or peripheral information storage medium 1340 andprocess the information to estimate at least one parameter of interest.Information processor 1300 may be located on the surface or downhole.

In some embodiments, shielding of the detectors may be implemented forneutrons and gamma rays. Gamma ray shielding prevents the detection ofgamma rays from behind the tool and from that originating within thetool. Neutron shielding prevents neutrons from reaching the detectorregions and inducing gamma rays. Combinations of neutron moderators,neutron absorbers, high hydrogen content epoxies, and high-densityhigh-Z materials are known to those skilled in the art.

While the foregoing disclosure is directed to the one mode embodimentsof the disclosure, various modifications will be apparent to thoseskilled in the art. It is intended that all variations be embraced bythe foregoing disclosure.

What is claimed is:
 1. A method for estimating at least one parameter ofinterest of a formation, comprising: conveying a carrier in a boreholeintersecting the formation, the carrier having disposed thereon at leastone energy source and at least one nuclear radiation detector;activating a volume of interest the formation with the at least oneenergy source; acquiring nuclear radiation information using the atleast one nuclear radiation detector in the borehole; estimating the atleast one parameter of interest by using at least one processor toseparate the nuclear radiation information into a plurality of nuclearradiation components each representing nuclear radiation from acorresponding different daughter radionuclide using a model relatingeach nuclear radiation component to an estimated nuclear density of thecorresponding parent nuclide; wherein the at least one parameter ofinterest is at least one of: (i) a silicon content, (ii) an oxygencontent, (iii) a sodium content, and (iv) an iodine content, and (v) aniron content, (vi) an aluminum content, and (vii) a magnesium content.2. The method of claim 1, wherein the at least one energy sourceincludes at least one of: (i) a pulsed neutron source and (ii) aconstant neutron source.
 3. The method of claim 1, wherein the nuclearradiation information includes a nuclear radiation count.
 4. The methodof claim 1, wherein the plurality of nuclear radiation componentsrepresent nuclear radiation from at least two different radionuclides.5. The method of claim 4, wherein the at least two radionuclides includeat least two of: (i) nitrogen-16, (ii) neon-23, (iii) sodium-24, (iv)magnesium-27, (v) aluminum-28, (vi) manganese-56, (vii) cobalt-58,(viii) cobalt-60, and (ix) iodine-128.
 6. The method of claim 1, whereinthe at least one nuclear radiation detector is in energeticcommunication with the volume of interest activated by the at least oneenergy source while the plurality of nuclear radiation components areabove a selected threshold.
 7. The method of claim 1, wherein theseparation is based on at least one of: (i) rates of radioactive decayand (ii) energy spectrum information.
 8. An apparatus for estimating atleast one parameter of interest of a formation, comprising: a carrierconfigured for conveyance in a borehole in the formation; at least oneenergy source operably connected to the carrier and configured toactivate a volume of interest in the formation; at least one nuclearradiation detector disposed on the carrier and configured to generateinformation representative of nuclear radiation from an the activatedvolume of interest; and an information processing device configured toestimate the at least one parameter of interest by separating thegenerated information representative of nuclear radiation into aplurality of nuclear radiation components each representing nuclearradiation from a corresponding different daughter radionuclide using amodel relating each nuclear radiation component to an estimated nucleardensity of the corresponding parent nuclide; wherein the at least oneparameter of interest is at least one of: (i) a silicon content, (ii) anoxygen content, (iii) a sodium content, and (iv) an iodine content, and(v) an iron content, (vi) an aluminum content, and (vii) a magnesiumcontent.
 9. The apparatus of claim 8, wherein the plurality of nuclearradiation components represent nuclear radiation from at least twodifferent radionuclides.
 10. The apparatus of claim 9, wherein the atleast two different radionuclides include at least two of: (i)nitrogen-16, (ii) neon-23, (iii) sodium-24, (iv) magnesium-27, (v)aluminum-28, (vi) manganese-56, (vii) cobalt-58, (viii) cobalt-60, and(ix) iodine-128.
 11. The apparatus of claim 8, wherein the at least oneenergy source includes at least one of: (i) a pulsed neutron source and(ii) a constant neutron source.
 12. The apparatus of claim 8, whereinthe carrier is configured to be deployed in the borehole.
 13. Theapparatus of claim 8, wherein the information representative of nuclearradiation comprises a nuclear radiation count.
 14. The apparatus ofclaim 8, where the information processing device comprises: a processor;and a memory storage medium.
 15. The method of claim 1, wherein themodel compensates for variations in exposure of the formation to the atleast one energy source over time.